So, I've used 关心 consistently with people - 关心别人, 关心我的妹妹, but can 关心 be used for object or a phrase??
Example for a phrase 我们关心的应该是房子应该有几间屋子?
Example for an object 吃饭时, 我关心的是调味。 长得怎么样, 我都不管。
关心 can be used for object. 关心国事 (duplicated with one of the answer here) is an example.
However, 关心 is only one of the many translation of "care". For example you could use the other translation of "care" in below sentence in blanket:
"吃饭时, 我关心(在意)的是调味。 样子怎么样, 我都不管"
I cares only about the seasoning (or taste) when I eat, and do not concern about it's appearance.
It's almost the same as care in English in terms of its usage.
You can replace 关心 with care in English too:
Other examples:
When 关心 is used in polite way, it has more broader meaning:
taking care of anything.